jmc

The center of the hyperbola is $(3,17).$ We also know that the distance from the center to each focus is $\sqrt{5^2+12^2}=13.$ Because the $x^2$ term has positive coefficient, the foci lie along the horizontal axis, so the two foci have coordinates $(3+13,17)=(16,17)$ and $(3-13,17)=(-10,17).$ Therefore, the answer is $\boxed{(16,17)}.$